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Superconductor Science and Technology

RCLSJ model correction and verification by a proposed test method for DFF’s high-frequency performance

Shuangmu Wang, Xi Gao, Jie Ren

Published Apr 14, 2025• 1 citation
Publisher

Abstract

Abstract The pursuit of high-speed response and precise reconstruction of phase reversal within Josephson junction constitutes the principal research objectives for the device model in the superconducting single flux quantum (SFQ) circuits. The proposing of the resistive-capacitive-inductive-shunted junction (RCLSJ) model by incorporating a shunted inductance on the classical resistive-capacitive-shunted junction (RCSJ) model, indeed achieves a more accurate description of the Current–Voltage ( I – V ) characteristics of Josephson junctions. However, the effectiveness of the RCLSJ model in dynamic simulations of SFQ circuits has not yet been verified. We proposed a simple and convenient test structure for D flip-flop (DFF) circuits to obtain the variation of its bias margin over a wide frequency sweep range. Post-simulations using the RCLSJ model were performed for DFF circuits. It was found that there are still matching problems between the simulations and tests, especially in the higher frequency region. Based on the junction area structure and layout application under the SIMIT-Nb03 process, a corrected RCLSJ model, designated as the RCLSJv model, was developed. This model mainly reassigns the parasitic inductance of the junction area and introduces correction coefficients by fitting the test data. The validity of the model has been verified through the comprehensive fitting of multiple sets of DFFs’ test data. In comparation with the RCSJ model, the deviation between the test and simulation results was successfully confined within 3%. Notably, in the frequency range above 60 GHz, the matching degree exhibits a remarkable enhancement, with an improvement factor ranging from 2 to 5 times.

DOI
10.1088/1361-6668/adcc61

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Abstract The pursuit of high-speed response and precise reconstruction of phase reversal within Josephson junction constitutes the principal research objectives for the device model in the superconducting single flux quantum (SFQ) circuits. The proposing of the resistive-capacitive-inductive-shunted junction (RCLSJ) model by incorporating a shunted inductance on the classical resistive-capacitive-shunted junction (RCSJ) model, indeed achieves a more accurate description of the Current–Voltage ( I – V ) characteristics of Josephson junctions. However, the effectiveness of the RCLSJ model in dynamic simulations of SFQ circuits has not yet been verified. We proposed a simple and convenient test structure for D flip-flop (DFF) circuits to obtain the variation of its bias margin over a wide frequency sweep range. Post-simulations using the RCLSJ model were performed for DFF circuits. It was found that there are still matching problems between the simulations and tests, especially in the higher frequency region. Based on the junction area structure and layout application under the SIMIT-Nb03 process, a corrected RCLSJ model, designated as the RCLSJv model, was developed. This model mainly reassigns the parasitic inductance of the junction area and introduces correction coefficients by fitting the test data. The validity of the model has been verified through the comprehensive fitting of multiple sets of DFFs’ test data. In comparation with the RCSJ model, the deviation between the test and simulation results was successfully confined within 3%. Notably, in the frequency range above 60 GHz, the matching degree exhibits a remarkable enhancement, with an improvement factor ranging from 2 to 5 times.
ENGLISH ABSTRACT: Rapid Single Flux Quantum (RSFQ) cells are key in the design of complex and applicable RSFQ electronic circuits. These cells are low-level circuit elements that are used repeatedly to build larger, applicable RSFQ circuitry. Making these cells simple to layout and manufacture, but reliable for extensive use demands a careful development process for RSFQ cells. Cell functionality is verified through simulations, thereafter the cell is laid out in special software packages. Inductance of on-chip superconductor structures is extracted through careful modelling with numerical field solver software. A cell library has been developed by incorporating existing or published cells after further analysis and optimization, as well as developing new cells. Cells that have been adapted into the library include the Josephson transmission line (JTL), Splitter, Merger, D-Flip Flop (DFF), T-Flip Flop (TFF), NOT, AND, OR and XOR, DC-SFQ and SFQ-DC and PTL Driver and Receivers. New cells include NOR, NAND and XNOR. The cells were designed for the IPHT’s RSFQ1D 1kA/cmª and Hypres’ 4.5kA/cmª processes. The cells in the library have good bias current operating margins obtained through simulations (> ±26%). All cells have all the parameters listed in the thesis including extracted inductance values. In order to have a complete and verified RSFQ cell library, cells have been sent for fabrication at IPHT and Hypres facilities. These cells can now be tested on-chip, in the laboratory, to establish functionality and practical bias current margins. All test signal patterns and bias currents required for testing are defined to allow co-workers or collaborators to test the cells.
The shunt resistors used in many Josephson junction circuits contain an inductive component that can significantly degrade high-frequency performance. Numerical simulations reveal complex dynamical behaviour, including relaxation oscillations, period-doubling sequences, and chaos, all of which are serious problems for applications as high-frequency sources and detectors. This complex AC behaviour creates features in the simulated DC current-voltage characteristics. Since these simulations closely match experimental data, they can be used to investigate the high-frequency AC behaviour of real junctions. Thus, we are able to use simple DC measurements to observe evidence of complex high-frequency dynamics. The inductance of the shunt branch can be accurately determined by comparing simulations to measurements. Simulations also allow us to map regions of the parameter space which exhibit complicated behaviour. These regions should be avoided when a nearly sinusoidal voltage waveform is desired, as is the case for Josephson junction-based oscillators.
We fabricated and tested high-temperature superconducting (HTS) rapid-single-flux-quantum (RSFQ) circuits using interface-engineered Josephson junction (IEJ). The characteristics of high-speed operation were examined by voltage-divider operation based on the toggle-flip-flop circuit. An operation at 155 GHz was obtained at 15 K and the proper functioning of the voltage divider was observed up to 27 K. Temperature dependence of the maximum operation speed was analyzed by circuit simulation with thermal-noise sources. To achieve higher speed operation using a Josephson junction with a higher I/sub c/R/sub n/ product, we also fabricated an RSFQ balanced comparator using IEJ; proper switching characteristics of the circuit was confirmed up to 190 GHz at 30 K. The bias condition dependencies were studied based on the circuit simulations in the relationship of the I/sub c/R/sub n/ product. The results of circuit simulation indicate that a Josephson junction with an I/sub c/R/sub n/ product of more than 0.7 mV is required for high-speed operation (100 GHz) in high-temperature range (30-40 K). We believe that the IEJ is a promising junction candidate for realizing high-speed operation in a high-temperature range.
Abstract\nThis diploma work is about Rapid Single Flux Quantum (RSFQ) circuits. This\nsupercoducting digital circuitry has the most promising properties in terms of speed and\npower consumption. The active elements of the RSFQ circuits are Josephson junctions (JJ).\nFor their fabrication low temperature superconducting niobium films are used. Today the\ndesign and fabrication of RSFQ circuits are done in a standardized way with well-defined\ndesign rules. Nevertheless, to design complicated circuits with more than several hundred\njunctions a lot of practical problems must be solved.\nDifferent aspects of the RSFQ circuits design process were investigated in this work.\nIn the theoretical part we propose a new, more realistic model of the Josephson junction for\nphysical simulation (which is necessarily used for design of every RSFQ gate) in order to\nimprove its quality and precision. The new model for the JJ includes additional inductances,\nwhich must reflect a specific environment of the junction layout. The influence of parameter\ndeviations was investigated in the simulation. As sources of the deviation we chose the\nspread of c (the Stewart-McCumber parameter) and that of the inductances. Then the\noperational margins of the basic elements of the RSFQ logic SR flip-flop were determined\nand compared with the prediction of the previously used model. To prove the results of\nsimulations we designed a test structure of the SR flip-flop, with c=1 and c=2 for the wellestablished\nHYPRES technology (USA).\nAnother part of the work is practical measurements. A test chip, containing chains of 100\nJosephson junctions was designed and measured in order to estimate the spread of critical\ncurrents in real technology.
Josephson junctions (JJs) with non-hysteretic I-V characteristic and high critical parameters are required for many applications; in particular, they are needed to create tunable THz range oscillators. We fabricated and studied shunted superconductor-insulator-superconductor (SIS) Nb-AlOx-Nb tunnel junctions with an area of about 1μm2, estimated their parameters, and compared them with theoretical models. To assess the performance of shunted junctions in the terahertz range, their characteristics were studied under the influence of a high-frequency signal; the estimated value of the characteristic voltage for the shunted junction at a high frequency is about 1 mV. To improve the circuit parameters, a new type of the shunting based on application of NIS junctions was proposed, which reduces the influence of parasitic inductance, expands the frequency range of the generator, and decreases the size of the structure. The JJs with a new type of shunting have been fabricated and studied. The niobium integrated circuits intended for matching the superconducting oscillator and an SIS junction as a microwave detector were designed, fabricated, and tested. Such structures are required for studying the spectral characteristics and analyzing the operation of the oscillator. The developed circuits have demonstrated efficient operation at frequencies from 300 to 700 GHz; the experimental results are in good agreement with the simulated characteristics. The results obtained will be implemented for further development of the THz range oscillators.
Abstract Josephson junctions based on superconducting materials are fundamental components for quantum detection, quantum communication and quantum computers. An accurate behavioral model of Josephson junctions is the prerequisite for predicting various superconducting circuits. In this study, We present a resistively and capacitively shunted junction (RCSJ) model-based behavioral-level model for the current-voltage characteristics of Josephson junctions. This model accurately predicts the current-voltage characteristics and their temperature dependencies of Josephson junctions made of different materials under three typical working modes: underdamped voltage-driven, overdamped current-driven, and underdamped current-driven. Additionally, it forecasts the critical current and superconducting energy gap characteristics with respect to temperature, as well as the constraint relationship between the shunt resistance, superconducting energy gap, and critical current. Comparing the measured data with the simulation predictions, the model has an average accuracy of 85.9%, which illustrates the reliability of the model.